UV Mesh Not Unwrapping Correctly
Your mesh is displaying dots along some of the edges. There are quite a few in the video, I marked a few below. These are actually face centres and show that there are hidden faces:



In edit mode select everything and choose W> Remove Doubles and this should get rid of the extra faces by merging close vertices.
From the blend file you supplied I also found many internal faces:



These need to be deleted (X> Faces). You can then also use Ctrl+N to recalculate normals to make sure all your faces are pointing the right way
 before unwrapping again.